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Finding the Third Proportional to 7,672 and 9,824

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Solution

The third proportional to 7,672 and 9,824 is: 12,579.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,672 : 9,824 = 9,824 : x
  2. Step 2: Convert to fraction form
    7,672/9,824 = 9,824/x
  3. Step 3: Cross multiply
    7,672x = 9,824 × 9,824
  4. Step 4: Simplify right side
    7,672x = 96,510,976
  5. Step 5: Solve for x
    x = 96,510,976/7,672
  6. Step 6: Final answer
    x = 12,579.64

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.